Jonah collects rainwater in a large barrel that weighs 30 pounds. When there are 10 gallons of water in the barrel, the total we
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Answer:
Step-by-step explanation:
We know that the plane travels at a <em>constant</em> speed of 14 km/min.
It passes over a radar station at a altitude of 11 km and climbs at an angle of 25°.
We want to find the rate at which the distance from the plane to the radar station is increasing 4 minutes later. In other words, if you will please refer to the figure, we want to find dc/dt.
First, let's find c, the distance. We can use the law of cosines:
We know that the plane travels at a constant rate of 14 km/min. So, after 4 minutes, the plane would've traveled 14(4) or 56 km So, a is 56, b is a constant 11. C is 90+20 or 115°. Substitute:
Evaluate:
Take the square root of both sides:
Now, let's return to our law of cosines. We have:
We want to find dc/dt. So, let's take the derivative of both sides with respect to t:
Since our b is constant at 11 km, we can substitute this in:
Evaluate:
Implicitly differentiate:
Divide both sides by 2c:
Solve for dc/dt. We already know that da/dt is 14 km/min. a is 56. We also know c. Substitute in these values:
Simplify:
Use a calculator. So:
And we're done!
